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Thread: Geometric Series Equivalence

  1. #1
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    Geometric Series Equivalence

    Hello,
    Why is this:
    Geometric Series Equivalence-1-divide_conquer_feb28march2-2017__pdf__page_9_of_19_.png

    Equivalent to this:
    Geometric Series Equivalence-1-divide_conquer_feb28march2-2017__pdf__page_9_of_19_.png

    Thank you.
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  2. #2
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    Re: Geometric Series Equivalence

    Since summations only work with integers, you can replace the log(n) parts with an integer, such as k. The write a proof by induction to show that

     \sum _{i=0} ^{k-1} 2^i = 2^k-1
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  3. #3
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    Re: Geometric Series Equivalence

    we expect \sum _{i=0}^{\text{Log} n-1} 2^i to be an integer

    but 2^{\text{Log} n}-1 is not necessarily an integer
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